Treasurer Joe Hockey has had to eat that silly remark in relation to fuel excise indexation.AAP/Nikki Short

On the third day, Joe Hockey laid on the mea culpa with a trowel. Appearing on Sydney radio to try to clean up after his disastrous Wednesday line about the poor and petrol, Hockey declared: “I am sorry about the words”.

“All of my life I have fought for and tried to help the most disadvantaged people in the community.” His comment had been “obviously insensitive”.

There was much more to the same effect, just to ram the message home. He didn’t have “evil in my heart” towards the disadvantaged. And he claimed to have been influenced in some way by “a lady at the lights at Cammeray [who] had a chat to me when I was crossing the road”; she said, “you have got to be true to yourself” (apparently intimating he’d stuffed up).

A few things may be observed about this performance. It was a political exercise so extravagant in nature and so late in coming that it invited cynicism. A (toned down) version should have been delivered on Wednesday, or Thursday. But it is good to see the Treasurer has had to eat that silly remark in relation to fuel excise indexation, when he said: “The poorest people either don’t have cars or actually don’t drive very far in many cases”.

Tony Abbott earlier on Friday had given Hockey a public clip over the ear. “Well, plainly, I wouldn’t say that,” the PM told a questioner. The Treasurer, known for a thin skin, could not miss that cruel word “plainly”. Abbott might as well have declared “Joe is so stupid”.

Some politicians turn the admission of error into a professional tool, but in Hockey’s case, it was the last line of defence, deployed by an amateur. Mind you, so many in this government are making big mistakes that if they owned up to them all they’d need an official confession box.

It is seriously difficult to understand how the government has come to be as bad as it is. Yes, it is hugely tribal, its ministers are convinced they know better than anyone else, and it has a faith in “spin” that has dramatically underestimated the public’s ability to judge for themselves.

Even taking all that into account, Hockey’s Wednesday blunder is hard to explain.

Why – leaving aside such provocative language – did he think he could get away with just talking about absolute amounts people spend on petrol, ignoring the relative impact on income groups?

Does he really believe the rest of the world – including (John Howard’s) “battlers” with lived experience of petrol prices, as well as economists who love quintiles and the like – wouldn’t be onto him in a flash?

Some are blaming weakness in Hockey’s office for what happened – he’s a couple down on senior staff – or even saying it’s about time for a ministerial reshuffle.

Staff are crucial, but they can’t be made an excuse. Hockey has plenty of ministerial experience, and Treasury to advise him. He only had to ask for all the relevant numbers, and think about the questions he’d get. Not complicated.

But while we’re on the subject of advisers, it is about time the PM announced who’ll be next head of Treasury. Abbott, with advice from his office, sacked Martin Parkinson nearly a year ago, and he departs in December. Treasury is undergoing a substantial downsizing. It requires certainty at a bureaucratic level. And Hockey needs a smooth transition in terms of departmental advice.

As for ministerial reshuffling: well, there would have to be quite a few demotions if performance were the yardstick. A reshuffle after a year and when things are so messy would be a sign of panic, create bad blood and instability, and not necessarily improve the situation. The idea of moving Hockey would be inconceivable, however poorly he’s travelling.

There is no one transforming solution to the muddle across the government. It just has to be worked at, minister by minister, issue by issue, driven by better leadership from the top.

And what about the top?

Abbott himself has had a strange week, looking like a commander-in-chief in search of a military role for the nation.

On returning from abroad he repaired on Friday to the Joint Operations Command centre near Canberra. “As you know, I’ve spent most of the last week overseas in connection with various operations,” he said. He referred to thanking, while in the Netherlands, Australians deployed for Operation Bring Them Home, his briefings in London on the threats posed by the Middle Eastern developments, and his stopover Al Minhad Airbase, from where Australia’s humanitarian airdrops for those at Mount Sinjar departed.

He continues to look for a further role for Australia. “While I certainly don’t envisage Australian combat troops in Iraq, we are consulting with our allies and partners on what Australia can usefully contribute to try to ensure that the situation in the Middle East improves rather than deteriorates,” he said.

This weekend Abbott will be on the Pollie Pedal, a familiar and comforting excursion. He gives the impression of a leader for whom the core task of governing and delivering has become very hard.